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On the Number of Positive Entries in the Powers of a Non-Negative Matrix

Published online by Cambridge University Press:  20 November 2018

N. Pullman
N. Pullman*
Affiliation:
McGill University
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A real matrix A is said to be non-negative if and only if none of its entries is negative. Suppose A is an r by r non-negative matrix. We want to examine:

  1. (A) The first power of A to maximize the number of positive entries in An,

  2. (B) For each 1 ≤ i ≤ r the first power of A to maximize the number of positive entries in the i-th row of An.

We shall call the former first power the index of A and the latter the i-th row index of A (index (i, A)).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 4 , December 1964 , pp. 525 - 537
Copyright
Copyright © Canadian Mathematical Society 1964

References

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